Problem: Simplify the following expression: $x = \dfrac{-9r}{-72r + 90}$ You can assume $r \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-9r = - (3\cdot3 \cdot r)$ The denominator can be factored: $-72r + 90 = - (2\cdot2\cdot2\cdot3\cdot3 \cdot r) + (2\cdot3\cdot3\cdot5)$ The greatest common factor of all the terms is $9$ Factoring out $9$ gives us: $x = \dfrac{(9)(-r)}{(9)(-8r + 10)}$ Dividing both the numerator and denominator by $9$ gives: $x = \dfrac{-r}{-8r + 10}$